"Jacqui Smith has resigned, 10 minutes ago," a Labour backbencher just told me in a corridor. "More dignified to resign before being sacked," he added.

I disagreed. A preemptive resignation removes Gordon Brown's room for manoeuvre in reshuffling his cabinet in his own way at his own time – if that is what he plans to do. "Not very comradely," I replied.

In the event the home secretary seems to have done a more sensible thing, which leaves the prime minister able to replace her as he wishes – with whoever he wants. It is a mug's game to guess Brown's mind. He may not know it himself. Prime ministers often improvise reshuffles and sometimes get their plans disrupted by awkward colleagues who say "No thanks".

What Smith has actually done is let it be known that she wishes to step down whenever the reshuffle takes place. There have been rumours to that effect for weeks; now it is more or less official. After the embarrassment of the dodgy videos charged to the taxpayer by her husband/assistant, Smith told Brown she had had enough in one of the toughest posts in any government.

It was never easy. Brown's decision to give her a major department when he first formed his government in June 2007 was always a gamble. Smith was the first woman in the post and had never previously run a department. First elected in Redditch in 1997 – always a West Midlands swing seat, she plans to defend it in what will be a tough contest – she had served as a junior minister, notably in education, and latterly as Tony Blair's chief whip.

The large, unwieldy Home Office had just been further subdivided, so that Jack Straw took control of the judiciary and prisons as justice secretary, leaving Smith with immigration, crime and the police. That was one of her problems; Straw is a highly experienced ex-home secretary with an easy capacity to bigfoot a novice.

The 42-day detention row, police pay (they heckled her), the showdown with mayor of London Boris Johnson over the fate of Met chief Sir Ian Blair (he won), the embarrassment over Damian Green MP's arrest (she didn't know, but should she have known?) ... they all cost her sleep at night. Then there was the row over the porn video and her taxpayer-funded second home. Voters learned more than they may have wanted to about the room Smith rents during the week from her sister in Peckham.

All of which must have made Smith wonder if high office was worth the strain of 24/7 policy pressures and the humiliation of being the butt of comedians' jokes. Plenty of ministers, the innocent as well as the tainted, are having this conversation with themselves as the expenses crisis drags on.

Who will get Smith's job? As I say, it's a mug's game. Some MPs suggest Brown may ask Alistair Darling to move across and sort out the department. As the cabinet's Mr Calm (the only survivor of 1997 apart from Brown himself and Straw) Darling moved to transport after that department blew up under Stephen Byers, then moved to the DTI and – in 2007 – succeeded Brown at the Treasury. He has helped to make it a more normal department again after the Brown-Balls hegemony.

But that suggestion raises two questions. If Darling is deemed to be damaged goods after repaying £668 worth of expenses, can he be given another department? And will he go quietly anyway? Many rate his quiet calm and lack of political ego – even though it infuriates those who say he does not make the government case robustly or cheerfully enough, let alone attack the deficiencies of the Tory alternative.

A third question immediately arises and has been answered in the negative already by many MPs and economic writers, who believe that if Ed Balls is the answer someone is asking the wrong question. The schools secretary is a divisive figure, widely mistrusted by MPs for his role as a Brown partisan, both as an MP and a special adviser to the then-chancellor. His record at schools is controversial, and so is the legacy he and Brown left at the Treasury on issues such as the pension fund raid and the regulatory regime that failed its Northern Rock test.

It underlines just how tricky a reshuffle might be in the best of times. These are not the best of times and no other obvious successor to Smith leaps to MPs' minds.